%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET071-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:09:11 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 76 ( 21 unt; 10 def)
% Number of atoms : 157 ( 47 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 153 ( 72 ~; 71 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f108,axiom,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
unordered_pair(x,y) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f117,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f120,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f124,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f125,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f131,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f190,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f242,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f249,plain,
unordered_pair(x,y) != null_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f250,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f251,plain,
~ member(y,universal_class),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f260,plain,
unordered_pair(y,x) != null_class,
inference(paramodulation,[status(thm)],[f242,f249]) ).
fof(f279,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f117,f120]) ).
fof(f354,plain,
! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ),
inference(resolution,[status(thm)],[f190,f125]) ).
fof(f447,plain,
! [X0] : ~ member(x,X0),
inference(resolution,[status(thm)],[f279,f250]) ).
fof(f448,plain,
! [X0] : ~ member(y,X0),
inference(resolution,[status(thm)],[f279,f251]) ).
fof(f600,plain,
( regular(unordered_pair(x,y)) = y
| regular(unordered_pair(x,y)) = x ),
inference(resolution,[status(thm)],[f354,f249]) ).
fof(f601,plain,
( regular(unordered_pair(y,x)) = x
| regular(unordered_pair(y,x)) = y ),
inference(resolution,[status(thm)],[f354,f260]) ).
fof(f629,definition,
( sQ21_spl
<=> regular(unordered_pair(x,y)) = x ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( ~ sQ21_spl
| regular(unordered_pair(x,y)) = x ),
inference(component_clause,[status(thm)],[f629]) ).
fof(f632,definition,
( sQ22_spl
<=> regular(unordered_pair(x,y)) = y ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f633,plain,
( ~ sQ22_spl
| regular(unordered_pair(x,y)) = y ),
inference(component_clause,[status(thm)],[f632]) ).
fof(f635,plain,
( sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f600,f629,f632]) ).
fof(f636,definition,
( sQ23_spl
<=> regular(unordered_pair(y,x)) = y ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f637,plain,
( ~ sQ23_spl
| regular(unordered_pair(y,x)) = y ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,definition,
( sQ24_spl
<=> regular(unordered_pair(y,x)) = x ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f640,plain,
( ~ sQ24_spl
| regular(unordered_pair(y,x)) = x ),
inference(component_clause,[status(thm)],[f639]) ).
fof(f642,plain,
( sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f601,f636,f639]) ).
fof(f752,plain,
( ~ sQ21_spl
| regular(unordered_pair(y,x)) = x ),
inference(paramodulation,[status(thm)],[f242,f630]) ).
fof(f762,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| y = x ),
inference(forward_demodulation,[status(thm)],[f637,f752]) ).
fof(f764,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| regular(unordered_pair(x,y)) = y ),
inference(backward_demodulation,[status(thm)],[f762,f630]) ).
fof(f766,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| unordered_pair(y,y) != null_class ),
inference(backward_demodulation,[status(thm)],[f762,f260]) ).
fof(f769,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| regular(unordered_pair(y,y)) = y ),
inference(forward_demodulation,[status(thm)],[f762,f764]) ).
fof(f770,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| regular(singleton(y)) = y ),
inference(forward_demodulation,[status(thm)],[f131,f769]) ).
fof(f772,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| singleton(y) != null_class ),
inference(forward_demodulation,[status(thm)],[f131,f766]) ).
fof(f825,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| member(y,singleton(y))
| singleton(y) = null_class ),
inference(paramodulation,[status(thm)],[f770,f190]) ).
fof(f828,definition,
( sQ35_spl
<=> singleton(y) = null_class ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( ~ sQ35_spl
| singleton(y) = null_class ),
inference(component_clause,[status(thm)],[f828]) ).
fof(f831,definition,
( sQ36_spl
<=> member(y,singleton(y)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f832,plain,
( ~ sQ36_spl
| member(y,singleton(y)) ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f834,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f825,f828,f831,f636,f629]) ).
fof(f843,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f832,f448]) ).
fof(f844,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f843]) ).
fof(f902,plain,
( ~ sQ22_spl
| member(y,unordered_pair(x,y))
| unordered_pair(x,y) = null_class ),
inference(paramodulation,[status(thm)],[f633,f190]) ).
fof(f903,definition,
( sQ44_spl
<=> unordered_pair(x,y) = null_class ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f904,plain,
( ~ sQ44_spl
| unordered_pair(x,y) = null_class ),
inference(component_clause,[status(thm)],[f903]) ).
fof(f906,definition,
( sQ45_spl
<=> member(y,unordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f907,plain,
( ~ sQ45_spl
| member(y,unordered_pair(x,y)) ),
inference(component_clause,[status(thm)],[f906]) ).
fof(f909,plain,
( ~ sQ22_spl
| sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f902,f903,f906,f632]) ).
fof(f910,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f907,f448]) ).
fof(f911,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f910]) ).
fof(f912,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f904,f249]) ).
fof(f913,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f912]) ).
fof(f914,plain,
( ~ sQ24_spl
| member(x,unordered_pair(y,x))
| unordered_pair(y,x) = null_class ),
inference(paramodulation,[status(thm)],[f640,f190]) ).
fof(f915,definition,
( sQ46_spl
<=> unordered_pair(y,x) = null_class ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f916,plain,
( ~ sQ46_spl
| unordered_pair(y,x) = null_class ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f918,definition,
( sQ47_spl
<=> member(x,unordered_pair(y,x)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f919,plain,
( ~ sQ47_spl
| member(x,unordered_pair(y,x)) ),
inference(component_clause,[status(thm)],[f918]) ).
fof(f921,plain,
( ~ sQ24_spl
| sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f914,f915,f918,f639]) ).
fof(f922,plain,
( ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f919,f447]) ).
fof(f923,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f922]) ).
fof(f924,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| ~ sQ35_spl
| null_class != null_class ),
inference(forward_demodulation,[status(thm)],[f829,f772]) ).
fof(f925,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| ~ sQ35_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f924]) ).
fof(f926,plain,
( ~ sQ21_spl
| ~ sQ23_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f925]) ).
fof(f927,plain,
( ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f916,f260]) ).
fof(f928,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f927]) ).
fof(f929,plain,
$false,
inference(sat_refutation,[status(thm)],[f635,f642,f834,f844,f909,f911,f913,f921,f923,f926,f928]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET071-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:55:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.061904 seconds
% 0.10/0.43 % CPU time: 0.193865 seconds
% 0.10/0.43 % Total memory used: 99.976 MB
% 0.10/0.43 % Net memory used: 99.872 MB
%------------------------------------------------------------------------------